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Is there an algorithm or program capable to find the volume resulting when a parallelepiped is intersected by an oblique plane?

What is most important, although, it's not specified in title is: given the resulting volume, it must be able to reverse the equations/algorithm to find the intersecting plane, wich is only specified by its normal vector

As a side note, it must be capable to run on iOS and Android devices, at an aceptable framerate when rendering at realtime on an interactive application

The following image depicts what is described above

Any help or comment is appreciated

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up vote 0 down vote accepted

This is a temporary solution I came up with.

When the parallelepiped's edges are not aligned with the coordinates axes. It requires sorting the parallelepiped's vertices from lower to upper in relation to the intersecting plane. Also it calculates a diferential volume, wich is used to integrate the intersecting volume, depending on the limits given by the parallelepiped's vertices

The following image shows when there is no parallelepiped edge that is aligned with the intersecting plane

The following can be used when four edges are aligned with the intersecting plane

I hope someone come up with an easier or less expensive one, in terms of required CPU cycles, but until now I think I'll use this one

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